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Stats I · All 2025 papers

BSMA1002 · 95 questions · 240 marks · 6 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

BSMA1002 · Statistics for Data Science I

All 2025 papers

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
MSQ: One or more options correct. Select all to score.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

Quiz 1 · 26 Oct 2025 (AN)Quiz 1

Q1MCQ2 Marks·Choose one option
Asked 5 times Key ↓
1. A7
2. B9
3. C8
4. D6
Q2MCQ3 Marks·Choose one option
Asked 4 times Key ↓
1. AYes
2. BNo
Q3MCQ3 Marks·Choose one option
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Q4MSQ2 Marks·Choose all correct options
Asked 5 times Key ↓
If addition and subtraction are meaningful operation for a variable, then the scale(s) of measurement of the variable could be:
1. ARatio
2. BNominal
3. COrdinal
4. DInterval
Q5MSQ2 Marks·Choose all correct options
Asked 4 times Key ↓
Which of the following statements correctly describe Descriptive and Inferential Statistics?
1. ADescriptive statistics uses probability theory to draw conclusions, while inferential statistics is represented through tables, charts, and graphs.
2. BInferential statistics involves using sample data to make generalizations or predictions about a population.
3. CBoth descriptive and inferential statistics only deal with numerical data, not categorical data.
4. DDescriptive statistics involves summarizing data using measures such as mean, median,and standard deviation.
Q6MSQ2 Marks·Choose all correct options
Key ↓
Choose the correct statement(s).
1. ACross-sectional data are collected at a single point in time across several individuals, firms, or regions etc.
2. BTime series data involve observations on a variable measured at a single point of time.
3. CNominal scale provides both labelling and meaningful ranking of categories.
4. DRatio scale has an absolute zero and allows for comparison of both differences and ratios between observations.
Q7NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q8NAT3 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q9NAT4 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q10NAT4 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q11NAT5 Marks·Write the number
Key ↓
There are 4 observations whose mean is 5 and population variance is 2.5. Two of the observations are known to be 4 and 6. Find the product of the remaining two observations.
Your answer:
Read the passage below, then answer Q12–Q13
Based on the above data, answer the given subquestions.
Q12MSQ2 Marks·Choose all correct options
Key ↓
Choose the correct statement (s).
1. ASince both branches have the same average, their performance is equally consistent.
2. BBranch A is more consistent than Branch B because its standard deviation is lower.
3. CBranch A delivers exactly 36 parcels every day, while Branch B’s daily deliveries fluctuate around 36.
4. DConsistency should be evaluated only on the basis of the mean.
Q13NAT2 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q14–Q15
Based on the above data, answer the given subquestions.
Q14MCQ2 Marks·Choose one option
Key ↓
Considering the data from all three years together, determine the overall market share (in percentage) of each movie category and identify which category has the highest share.
1. AAction
2. BDrama
3. CComedy
4. DSci-fi
Q15MCQ2 Marks·Choose one option
Key ↓
The manager wants to analyze the market shares (%) of Action and Drama movies for each year. Determine the maximum absolute percentage difference between the market shares of these two categories over the given years.
1. A10%
2. B40%
3. C50%
4. D20%

End Term · 31 Aug 2025 (FN)End Term

Q16MCQ3 Marks·Choose one option
Asked 4 times Key ↓
Consider the dataset 10, 27, 32, 15 and 22. A new dataset is obtained by subtracting 3 from every observation. Compute the value of (70th percentile of new dataset) - (30th percentile of the old dataset).
1. A-3
2. B9
3. C3
4. D-9
Q17MSQ1 Mark·Choose all correct options
Asked 2 times Key ↓
Which of the following statements is/are true?
1. AMedian can be measured for a categorical variable only if the variable is nominal.
2. BMode can not be defined for categorical data.
3. CThere can be more than one mode for a data.
4. DThe sum of relative frequencies of all the observations in a given data set is always equal to 1.
Q18MSQ3 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
5. E
Q19MSQ3 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Q20NAT3 Marks·Write the number
Key ↓
Your answer:
Q21NAT3 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q22NAT3 Marks·Write the number
Key ↓
Your answer:
Q23NAT3 Marks·Write the number
Key ↓
If two fair dice are thrown, what is the probability that the sum is either 4 or 9? Enter the answer correct to two decimal places.
Your answer:
Q24NAT3 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q25–Q26
Based on the above data, answer the given subquestions.
Q25NAT2 Marks·Write the number
Asked 2 times Key ↓
Find the value of c such that X has a valid pmf. Enter the answer correct to one decimal place.
Your answer:
Q26NAT3 Marks·Write the number
Asked 4 times Key ↓
Find the value of Var(X). Enter the answer correct to two decimal places.
Your answer:
Read the passage below, then answer Q27–Q28
Based on the above data, answer the given subquestions.
Q27MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q28NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q29–Q30
Based on the above data, answer the given subquestions.
Q29NAT2 Marks·Write the number
Key ↓
What is the probability that a randomly selected box contains at most 1 defective item? Enter the answer correct to one decimal place.
Your answer:
Q30NAT3 Marks·Write the number
Asked 5 times Key ↓
Your answer:

End Term · 31 Aug 2025 (AN)End Term

Q31MCQ2 Marks·Choose one option
Key ↓
Find the number of rearrangements of the letters in the word COMMITTEE.
1. A
2. B
3. C
4. D
Q32MCQ2 Marks·Choose one option
Asked 3 times Key ↓
1. A0.6
2. B0.8
3. C0.2
4. D1
Q33MSQ2 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q34MSQ2 Marks·Choose all correct options
Asked 6 times Key ↓
Which of the following statement(s) is/are incorrect?
1. AThe annual income of 1000 individuals surveyed for year 2024 is an example of time-series data.
2. BThe brand of a smartphone used by students is a categorical variable.
3. CEducational qualifications such as elementary, secondary, and higher secondary has an ordinal scale of measurement.
4. DMaking predictions about population behavior based on sample data is a part of Descriptive Statistics.
Q35NAT3 Marks·Write the number
Key ↓
Your answer:
Q36NAT3 Marks·Write the number
Key ↓
Your answer:
Q37NAT3 Marks·Write the number
Asked 4 times Key ↓
The number of vehicles passing through a highway toll booth in a minute follows a Poisson distribution with mean λ = 4. Find the probability that at most two vehicle pass through highway toll booth in a minute. Enter the answer correct to two decimal places. (Use : e^4 = 54.60, e^(1/4) = 1.28, e^(-4) = 0.02, e^(-1/4) = 0.78)
Your answer:
Q38NAT3 Marks·Write the number
Key ↓
Your answer:
Q39NAT3 Marks·Write the number
Asked 4 times Key ↓
Consider the dataset 10, 27, 32, 15 and 22. If we subtract 3 from all observations, find the difference between IQR of the new dataset and the old dataset.
Your answer:
Read the passage below, then answer Q40–Q41
Based on the above data, answer the given subquestions.
Q40MCQ1 Mark·Choose one option
Key ↓
Find the range of X.
1. A{20, 10, 30, 40}
2. B{−20, 10, 30, 40}
3. C{−20, 0, 10, 30, 40}
4. D{0, 10, 20, 30, 40}
Q41MCQ4 Marks·Choose one option
Key ↓
Find the PMF of X.
1. A
2. B
3. C
4. D
Read the passage below, then answer Q42–Q43
Based on the above data, answer the given subquestions.
Q42NAT3 Marks·Write the number
Key ↓
Find the value of a.
Your answer:
Q43NAT2 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q44–Q45
A box contains 4 red balls and 5 blue balls. Three balls are drawn at random without replacement. Based on the above data, answer the given subquestions.
Q44NAT3 Marks·Write the number
Key ↓
What is the probability that all three balls drawn are of the same colour? Enter the answer correct to two decimal places.
Your answer:
Q45NAT4 Marks·Write the number
Key ↓
Let X denote the number of red balls selected. Find the value of P(X = 3 | X ≥ 1) Enter the answer correct to two decimal places.
Your answer:

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Q46MCQ2 Marks·Choose one option
Key ↓
1. A0.2
2. B0.1
3. C1
4. D0.3
Q47MCQ3 Marks·Choose one option
Asked 3 times Key ↓
A survey of 800 students shows that 65% like reading and 50% like painting. If each student likes at least one of the two activities, how many students like painting but not reading?
1. A240
2. B400
3. C280
4. D120
Q48MCQ3 Marks·Choose one option
Key ↓
How many numbers greater than 10,000 can be formed using the digits 0, 2, 5, 4, 6, 8 without repetition?
1. A600
2. B120
3. C240
4. D1200
Q49NAT2 Marks·Write the number
Key ↓
In a quiz competition, eight students are competing, each assigned a roll number from 1 to 8. What is the probability that only students with prime-numbered roll numbers (i.e., 2, 3, 5, 7) secure the top four ranks, in any order? Enter the answer correct to three decimal places.
Your answer:
Q50NAT2 Marks·Write the number
Key ↓
A company has 15 offices and wants to set up two-way communication between every pair of offices. However, the 3 smallest offices will not have direct communication with one another, though each of them can still connect directly with the remaining offices. How many communication channels are needed in total?
Your answer:
Q51NAT3 Marks·Write the number
Key ↓
A group of 4 teachers and 4 students is to be seated around a circular table for a discussion. They decide that all students must sit together. Find the number of ways they can be seated around the table such that all students are sitting together.
Your answer:
Q52NAT3 Marks·Write the number
Key ↓
A basket contains 5 red balls and 4 green balls. If 3 balls are to be selected at random without replacement, in how many ways can the balls be selected such that at least one green ball is included?
Your answer:
Q53NAT3 Marks·Write the number
Key ↓
How many 5-digit numbers can be formed using the digits 0, 2, 3, 4, and 7 where digits may be repeated such that the number is divisible by 2 ?
Your answer:
Q54NAT3 Marks·Write the number
Asked 3 times Key ↓
A box C contains 3 white balls and 2 black balls, while box D contains 4 white balls and 3 black balls. One ball is randomly selected from box C and transferred to box D. After the transfer, one ball is drawn at random from box D. What is the probability that the ball drawn from box D is black? Enter the answer correct to three decimal places.
Your answer:
Q55NAT3 Marks·Write the number
Asked 3 times Key ↓
In how many different ways can the letters of the word ‘ARTICLE’ be arranged such that all the vowels always come together?
Your answer:
Q56NAT3 Marks·Write the number
Key ↓
A committee of 3 people is to be formed from a group of n people. The number of possible committees in which two particular people A and B are both included together is 7. Find the number of ways in which committee can be formed.
Your answer:
Read the passage below, then answer Q57–Q58
Based on the above data, answer the given subquestions.
Q57MCQ2 Marks·Choose one option
Key ↓
What is the probability that exactly 2 gold and 1 silver coin are drawn in the first draw?
1. A
2. B
3. C
4. D
Q58MCQ3 Marks·Choose one option
Key ↓
Given that the first draw results in 2 gold coins and 1 silver coin, what is the probability that the second draw results in exactly 2 silver coins and at least 1 gold coin?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q59–Q60
Based on the above data, answer the given subquestions.
Q59MSQ3 Marks·Choose all correct options
Key ↓
Which of the following option(s) is / are correct?
1. AEvents E_1 and E_2 are mutually exclusive.
2. BEvents E_1 and E_2 are independent.
3. CThere is only 1 favorable outcome for event E_2.
4. DAll of these
Q60NAT2 Marks·Write the number
Key ↓
How many panels include at least one Mathematics student?
Your answer:

End Term · 13 Apr 2025 (FN)End Term

Q61MCQ1 Mark·Choose one option
Key ↓
A box contains 10 marbles, 6 of which are red and 4 are blue. A sample of 4 marbles is randomly selected without replacement. Let the random variable X represent the number of red marbles in the selected sample. Identify the distribution of X.
1. AHypergeometric
2. BPoisson
3. CBinomial
4. DUniform
Q62MCQ2 Marks·Choose one option
Asked 4 times Key ↓
1. A64
2. B18
3. C16
4. D32
Q63MCQ3 Marks·Choose one option
Key ↓
1. A318240
2. B78000
3. C18720
4. D39000
Q64MCQ3 Marks·Choose one option
Asked 2 times Key ↓
A group of 7 people (A, B, C, D, E, F, G) is to be seated in a row for a photograph. Find the number of possible arrangements such that D and E cannot sit next to each other.
1. A3600
2. B4320
3. C5040
4. D720
Q65MSQ2 Marks·Choose all correct options
Asked 5 times Key ↓
Which of the following option(s) is/are correct for a variable with an ordinal scale of measurement?
1. AThe data can be arranged in a meaningful order.
2. BArithmetic operations like addition and subtraction are valid.
3. CThe intervals between values are equal and meaningful.
4. DThe mode and median can be determined, but not the mean.
Q66NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q67NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q68NAT3 Marks·Write the number
Asked 4 times Key ↓
A call center receives customer calls and the number of calls received per hour follows a Poisson distribution with a mean rate of 6 calls per hour. What is the probability that at most 2 calls are received in 30 minutes? Enter the answer correct to two decimal places.
Your answer:
Read the passage below, then answer Q69–Q70
Consider a dataset such as 8, 12, 16, 24, and 20. Suppose we multiply all observations by 3. Based on the given information answer the subquestions.
Q69NAT2 Marks·Write the number
Asked 4 times Key ↓
What will be the 25th percentile of the new dataset?
Your answer:
Q70NAT2 Marks·Write the number
Asked 4 times Key ↓
Find IQR of the new dataset.
Your answer:
Read the passage below, then answer Q71–Q72
Based on the above data, answer the given subquestions.
Q71MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q72MCQ2 Marks·Choose one option
Key ↓
1. A0.023
2. B0.230
3. C0.346
4. D0.035
Read the passage below, then answer Q73–Q74
Based on the above data, answer the given subquestions.
Q73NAT2 Marks·Write the number
Asked 2 times Key ↓
If the probability that the vendor sells exactly 2 items in a day is 0.30, then find the value of a. Enter the answer correct to two decimal places.
Your answer:
Q74NAT2 Marks·Write the number
Key ↓
What is the probability that the vendor sells at least 2 items in a day? Enter the answer correct to two decimal places.
Your answer:
Read the passage below, then answer Q75–Q76
Based on the above data, answer the given subquestions.
Q75NAT3 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q76MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q77–Q78
The time taken by a coffee machine to brew a cup of coffee is uniformly distributed between 2 and b minutes. Based on this information, answer the given subquestions:
Q77NAT2 Marks·Write the number
Key ↓
If the expected time for the coffee machine to brew a cup of coffee is 8.5 minutes, then find the value of b.
Your answer:
Q78MCQ3 Marks·Choose one option
Asked 4 times Key ↓
If the coffee machine has been brewing for more than 6 minutes, what is the probability that it will finish brewing between 6 and 10 minutes?
1. A
2. B
3. C
4. D

End Term · 13 Apr 2025 (AN)End Term

Q79MCQ2 Marks·Choose one option
Asked 2 times Key ↓
1. A21.5
2. B20
3. C5.38
4. D5
Q80MCQ3 Marks·Choose one option
Asked 3 times Key ↓
1. A0.15
2. B0.25
3. C0.75
4. D0.10
Q81MSQ2 Marks·Choose all correct options
Key ↓
Consider the following statements related to permutation and combination. Which of the following is/are true?
1. A
2. B
3. C
4. D
Q82MSQ2 Marks·Choose all correct options
Asked 3 times Key ↓
A surveyor collects data on the electricity bills of 100 randomly selected households in a particular month. Which of the following statements about this data is/are correct?
1. AThe electricity bill in rupees is a continuous variable.
2. BThe data collected represents cross-sectional data.
3. CThe electricity bill in rupees is a categorical variable.
4. DThe data collected represents time-series data.
Q83MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
A customer support center tracks the time agents take to resolve customer queries. Let X (in minutes) represent the resolution time, which follows an exponential distribution with an average resolution time of 2 minutes. Which of the following option(s) is/are true?
1. A
2. B
3. C
4. D
Q84NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q85NAT3 Marks·Write the number
Asked 2 times Key ↓
A group of 7 people (A, B, C, D, E, F, G) is to be seated in a row for a photograph. The following conditions must be satisfied: • A and B must always sit next to each other. • D and E cannot sit next to each other. What is the total number of valid arrangements under these conditions?
Your answer:
Q86NAT3 Marks·Write the number
Asked 3 times Key ↓
At a university, 60% of the students are enrolled in science programs, while 40% are enrolled in arts programs. Among science students, 25% participate in research projects, whereas 15% of arts students participate in research project. If a student is chosen at random, what is the probability that he/she participates in a research project? Enter the answer correct to two decimal places.
Your answer:
Q87NAT3 Marks·Write the number
Asked 5 times Key ↓
The total number of observations in a dataset is 8. If the mean of first 4 observations is 12 and the mean of all 8 observations is 18, then find the mean of last 4 observations.
Your answer:
Read the passage below, then answer Q88–Q89
A shopping mall conducted a survey among 150 customers to study the relationship between age group and preferred payment method (Cash or Digital). The collected data is shown in the table Q.1:
Based on the above data, answer the given subquestions.
Q88NAT2 Marks·Write the number
Key ↓
What proportion of the total customers prefer digital payments? Enter the answer correct to two decimal places.
Your answer:
Q89NAT1 Mark·Write the number
Key ↓
How many customers of age between 18 to 45 prefer cash payment?
Your answer:
Read the passage below, then answer Q90–Q91
The probability mass function of a discrete random variable X is given by,
Based on the above data, answer the given subquestions.
Q90MCQ2 Marks·Choose one option
Asked 5 times Key ↓
Find the value of E(6X − 2).
1. A1
2. B4
3. C6
4. D8
Q91NAT2 Marks·Write the number
Asked 4 times Key ↓
Find the value of V (3X − 4).
Your answer:
Read the passage below, then answer Q92–Q93
Let X represent the time a student takes to complete a test, which follows a uniform distribution between 45 and 75 minutes. Using this information, answer the given subquestions.
Q92NAT2 Marks·Write the number
Key ↓
Your answer:
Q93MCQ3 Marks·Choose one option
Asked 4 times Key ↓
Given that a student has already spent 60 minutes on the test, what is the probability that they will take more than 65 minutes to complete it?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q94–Q95
A small game involves spinning a wheel that has an equal chance of landing on one of four colors: Red, Blue, Green, or Yellow. Let the random variable X represent the number of times the wheel lands on Red in three independent spins.
Based on the above data, answer the given subquestions.
Q94MCQ3 Marks·Choose one option
Asked 3 times Key ↓
Find probability that the wheel lands on red exactly 2 times out of the three spins.
1. A
2. B
3. C
4. D
Q95NAT2 Marks·Write the number
Asked 2 times Key ↓
Find the value of E(X). Enter the answer correct to two decimal places.
Your answer:

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q1B

Q2A

Q3D

Q4A, D

Q5B, D

Q6A, D

Q70.8

Q872

Q9175

Q100

Q1121

Q12B, C

Q13256

Q14B

Q15D

Q16B

Q17C, D

Q18A, E

Q19A, B, C

Q2010

Q210.5 to 0.7

Q2260

Q230.17 to 0.21

Q240.73 to 0.79

Q250.2

Q260.73 to 0.79

Q27B

Q282

Q290.3

Q3022

Q31D

Q32B

Q33B, C

Q34A, D

Q357

Q361.65 to 1.69

Q370.26

Q380.7

Q390

Q40B

Q41D

Q426

Q430.75

Q440.14 to 0.2

Q450.02 to 0.08

Q46B

Q47C

Q48D

Q490.011 to 0.017

Q50102

Q51576

Q5274

Q531500

Q540.422 to 0.428

Q55720

Q5684

Q57C

Q58B

Q59A, C

Q6019

Q61A

Q62A

Q63B

Q64A

Q65A, D

Q663.64 to 3.7

Q670.51 to 0.57

Q680.39 to 0.45

Q6936

Q7024

Q71B

Q72C

Q730.43 to 0.47

Q740.53 to 0.57

Q7534

Q76B

Q7715

Q78A

Q79D

Q80D

Q81A, D

Q82A, B

Q83A, B, D

Q8435

Q85960

Q860.18 to 0.24

Q8724

Q880.54 to 0.6

Q8945

Q90B

Q9118

Q9250

Q93B

Q94A

Q950.73 to 0.77

Questions and answer keys are reproduced from the official IIT Madras BS papers. BTechi is not affiliated with IIT Madras.